HVEV RUN 3 AT NEXUS
3.5 Data Processing
Using the known DCRC design, the recorded ADC data was converted to units of current through each TES channel. Further use of the data required processing it to identify the timing and amplitude of individual events as well as converting the current signal to event energies. In the following section, we will discuss how the Run 3 data was processed. This includes event identification (triggering) and filtering to reduce non-signal-like backgrounds.
3.5.1 Triggering
Within each half second of data, events were identified using Gaussian-derivative- filter (GF) triggering. First, data was filtered using a kernel with the shape of a differentiated Gaussian. Then, events were identified as times when the GF-filtered data went above a set trigger threshold. The differentiated-Gaussian shape was chosen for its ability to distinguish events close in time. Figure 3.12 from the low-
energy event investigation shows GF triggering effectively identifying individual events within a burst [45]. For Run 3, a Gaussian with 25.6µs standard deviation was used. With this filtering, events as close as ∼120µs could be distinguished.
Figure 3.16 compares Run 3’s GF to a matched filter (the type used in Run 2) using Run 3 data.
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Time (samples) 0.10
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Current (A)
Raw trace
Filtered with GF Filtered with MF Trigger threshold
Figure 3.16: An example burst event in the Run 3 data. We see that the Gaussian- derivative filter (GF) works well for identifying individual events in the burst via a post-filter threshold trigger. The matched filter (MF) cleans the trace but is ineffective at identifying events that are near in time.
When tested using laser data, GF-trigger efficiency was observed to go to unity for event energies >35 eV. This indicated that only an insignificant number of events were missed in the energy range used for the limit setting (see Section 3.12.1).
Events were identified separately in each detector using the combined signal from inner and outer channels (relatively weighting each channel as described in Section 3.6). Each event’s associated trace (the subset of time used for further analysis) was defined to include 6.55 ms to either side of the event’s filtered maximum.
3.5.2 Optimal Filtering
The Gaussian-derivative filter was only applied when identifying event triggers. For the rest of the analysis, event traces were filtered using the Optimal Filtering (OF) method (see [47] and Section 4.2.1). This method creates a frequency-space filter proportional to the expected signal weighted by the measured noise. The relative weighting preferentially preserves frequencies consistent with signal and devalues
Figure 3.17: The Run 3 trigger efficiency fit to an error function. Trigger efficiency was calculated by applying the GF-trigger to the laser data and calculating the fraction of events identified. Efficiency goes to zero for low-energy events since they cannot be identified above noise. The important result is that efficiency goes to unity (with little uncertainty) above∼30 eV (well below the first quantized peak at 100 eV).
frequencies consistent with noise. The OF used for Run 3 was normalized such that signal-like events would have the same amplitude before and after filtering.
For Run 3, the expected-signal template for each detector was calculated using laser-generated events from January 11th. The events were aligned in time using the laser TTL signal and averaged to lower random noise. Events from traces with an overall slope were removed to avoid polluting the template with longer-timescale changes in signal. In total, just under 20k events were averaged for each detector.
A low-pass Butterworth filter was used to remove remaining high-frequency noise.
Specifically, a 10th-order forward-backward filter with 60 kHz cutoff frequency was used for NF-C and NF-H. The same type of filter was used for R1 but with a 20 kHz cutoff due to its higher noise. The NF-C template can be seen in Figure 3.18. The frequency-domain reduced𝜒2, which quantifies discrepancies between data and the fitted OF template (in frequency space), was observed to be distributed about 1 for the Run 3 science data. This indicated that the laser-derived template was a good fit to the non-laser science data. The reduced 𝜒2 was also stable throughout the run, confirming that the signal shape did not change over time. The signal stability was attributed to the stable temperature and channel biasing maintained throughout the
run.
Figure 3.18: NF-C signal template
The raw and Butterworth-filtered signal template for the NF-C detector. (Left) The template in time space.
Each time sample is equivalent to 1.6µs. (Right) The template in frequency space. We see that the Butterworth filter effectively removes high-frequency noise.
While each detector’s expected-signal template was constant throughout the run, the noise was re-estimated for every minute of data taking. For each minute, noise was calculated in each detector using traces triggered at random times. Randomly triggered traces with unusual mean, standard deviation, slope, or skewness were removed from the calculations. Typical noise power spectral densities (PSDs) for NF-C can be seen in Figure 3.19.
By combining templates and noise measurements, OFs were calculated for each detector and every minute of data taking. Each trace was then filtered using the appropriate OF. For each event, the amplitude of the filtered trace at the time of triggering was recorded as a reduced quantity (RQ) labeled the "OF0 amplitude".
The reduced𝜒2of the fit between data and template at that time was recorded as the
"OF0𝜒2". Amplitude and reduced𝜒2RQs were also recorded with the event timing allowed to shift to achieve the best fit (lowest𝜒2) within±24µs of the trigger. These RQs were given the prefix "OFL" (OF with a Limited time shift). It is a feature of the OFL RQs that the maximum filtered amplitude in a trace will occur at the time that produces the lowest 𝜒2fit [47]. Therefore, the OFL values also correspond to the highest filtered amplitude within the allowed time region. For events with little to no signal, this caused the OFL RQs to instead find the largest noise fluctuation resulting in biases in pulse height near zero amplitude. Accordingly, the analysis used OF0 values for sub-1𝑒−ℎ+events.
Figure 3.19: Typical noise power spectral density (PSD) in the NF-C detector. Many partially transparent PSDs are plotted on top of each other. Their similarity makes individual PSDs difficult to distinguish. Each PSD is calculated using random triggers from one minute of data taking. The noise was very stable, so the plot looks much like a single PSD.